CHEM 342. Spring 2002. Problem Set #8. Mortimer Chapters 19, 20.
Note: Please note that B 
h
8 2 cI
where B is expressed in cm1; and B 
h
8 2 I
where
B is expressed in Hz.
Rotating Diatomic Molecules
1. For a diatomic molecule in a 1  electronic state, we observe a microwave transition
from J = 1 to J = 2 in the presence of an electric field. How many lines will appear in the
spectrum?
2. Which of the following diatomic molecules have a rotational microwave spectrum: IF,
O 2 , KCl, Cl 2 .
3. Calculate the bond length of
  1.14 10 26 kg .
12
C 16O using B  1.9302 cm 1 and the reduced mass is
Vibrating Diatomic Molecules
4. Which of the following vibrational transitions will be observed for a diatomic molecule
(treated as a harmonic oscillator): v = 1 to v = 3; v = 2 to v = 3; v = 5 to v = 4.
5. Calculate the frequency of the J = 3 to J = 4 transition in the pure rotational absorption
spectrum of 14 N 16O . The equilibrium bond length is 115 pm. Assume no centrifugal distortion.
The mass of a nitrogen atom is 14.003 amu; the mass of an oxygen atom is 15.995 amu; and the
conversion factor is 1.6605 10 27 kg/amu .
Rotation of Polyatomic Molecules
6. Identify the molecules that will exhibit a pure rotational absorption microwave
spectrum: N 2 O, NO2 , CClF3 , NF3 , SF6 , CH 4 , CO2 .
7. What information about the molecular geometry for N 2 O can be determined from
knowing that a pure rotational absorption spectrum is observed for this molecule?
8. The moment of inertia about an axis perpendicular to the principal axis ( I  ) for NH 3
is 2.82  10 47 kg m 2 . There are different types of rigid rotors: linear, spherical top, prolate
symmetric top, oblate symmetric top, asymmetric top. Which type of rotor is NH 3 ? Calculate
the separation (expressed in cm 1 ) of the pure rotational spectrum lines for NH 3 . Hint: The
moment of inertia about the principal axis is given by I ll  2m H R 2 1  cos  , where the mass of
a hydrogen atom = mH = 1.6735 10 27 kg ; the N-H bond length = R = 1.014 10 10 m ; and the
bond angle is 106.78. The moment of inertia about the principal axis is I ll .
9. The molecule CClF3 is a prolate symmetrical top with A  0.1908 cm 1 and
B  0.1111 cm 1 . Calculate the energy corresponding to J = 2 and K = 1.
Vibration of Polyatomic Molecules
10. Consider the vibrational mode that corresponds to the uniform expansion of the
benzene ring. Is it infrared active?
CHEM 342. Spring 2002. Problem Set #8. Mortimer Chapters 19, 20.
Raman Spectroscopy
11. Explain the difference between Stokes and anti-Stokes lines in Raman Spectroscopy.
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